I guess it depends on how well they’ve coped with being picked up in the past.
If they’ve wiggled and tried get free, I’d avoid handling them. Also, if they get stressed, it will add to stress of the spay.

Some handling is unavoidable if you’re having to give post op pain med or assist feeding & drinking. If you can, keep them on the floor to do this.

To check the incision site, you can tempt them to stand on hind legs by offering a treat above the head. Best if they support themselves against a pen or cage sides with front paws when you do this. They probably won’t do this the 1st day after surgery but later in the week they might.

If that trick doesn’t work, you’ll probably have to pick them up briefly to check. I’d do this while sitting on the floor.

If it’s a cuddle you or they are wanting & they’re ok with it, I’d lay or sit on the floor & pop them on top.
Generally, buns don’t like cuddles so best leave them be even though we want to console them after surgery.

Have they already had the Op?

Oh ok. I would think handling now should be ok… I’m sure your vet clinic wouldn’t mind a quick call to verify.

Most females want to be left alone, are not interested in eating at all, and will sit quietly in a back corner of the cage (or wherever in the house they feel they will be bothered the least). Try not to pick up or bother her much for the first 4 days. Females take it harder.
http://rabbit.org/faq-spaying-and-neutering/